Another feature of the solution Eq.(REF ) is, for the degenerate solution where \(\kappa _2=\kappa _1\) , and with the limit, \(\kappa _1 \rightarrow 0\) , while we get a second-order rogue wave solution [1]}, [2]}, with \(\kappa _2=\sqrt{4-\kappa _1^2}\) , (Eq.(REF )), we have the freedom to take two such limits: one is \(\kappa _1 \rightarrow 0\)  and the other is \(\kappa _1 \rightarrow 2\) . For each limit, we obtain a first-order rogue wave solution. Alternatively, if we take these limit on Eq.(REF ), we get:
\(\nonumber \lim _{\kappa _1 \rightarrow 0} \psi _2(x,t)&=&\lim _{\kappa _1 \rightarrow 2} \psi _2(x,t)\\&=& \psi _1(x,t)=\left(\frac{G_1+i \,H_1}{D_1}-1\right) e^{i x}\) 
